Your glue records are correct. That isn't the issue.
The problem is, you didn't configure the localroute.net domain, itself, to actually use the white label servers, even though you've configured the global authoritative servers at the top level of the .net domain (the gTLD servers) -- via the registrar -- to believe that you did.
If you open up the Route 53 console, and highlight that hosted zone for localroute.net (don't click on the actual domain name, just on the row in the table), I believe you'll find that the 4 nameservers listed on the right side of the screen are not the correct Route 53 servers -- they don't correspond to the same 4 IP addresses that match your 4 white label servers. They should be these:
ns-1455.awsdns-53.org. 205.251.197.175
ns-1003.awsdns-61.net. 205.251.195.235
ns-207.awsdns-25.com. 205.251.192.207
ns-1570.awsdns-04.co.uk. 205.251.198.34
The localroute.net hosted zone -- I suspect you'll find -- will not be using these, but tsf-test.com will be, because it's correct.
But those are the equivalent servers for ns1-ns4, which allegedly is authoritative for localroute.net... yet if you ask those specific Route 53 servers about localroute.net, they have no idea what you're talking about.
;; ->>HEADER<<- opcode: QUERY, status: REFUSED, id: 21284
^^^^^^^
So, assuming the above is accurate, how do you fix it?
The NS records in the hosted zone itself are irrelevant if values corresponding to different IP addresses are shown here.
I'm guessing you may have edited the NS records for the localroute.net zone, and you can't arbitrarily do that. It doesn't work that way. The hosted zone must already be on those name servers, or the change doesn't accomplish anything useful.
You'll need to create a new hosted zone for localroute.net using the same process that you used to create tsf-test.com -- so that it is associated with the white label name servers. You don't have to delete the old one first -- you can delete it later. Create the zone, populate the records, and the issue should be resolved.
Best Answer
As far as I can tell, your namecheap config is right, but you need to configure a zone for
coolpatterns.neton your DNS as well, so that the DNS server will answer queries for that domain. It just answers the following when I just tried it withnslookup: